Calculators have been easily accessible for classroom use for over 30 years. Graphing calculators, on the other hand, have only been available for about 20 years and have been an integral part of the curriculum for the majority of classrooms across the country for just over 10 years (Singletary, 2009). Graphing calculators are capable of plotting graphs on the screen, graphing equations, and solving multiple equations simultaneously. They also have download-able programs available that can solve more complex equations (International Society for Technology in Education, 2008). These types of calculators are mostly used for higher level math, such as Algebra II and Calculus.
For about a decade, there has been an argument whether or not calculators should be used during math testing. There are still debates between teachers and states on this issue, but many standardized tests and college entrance exams allow the use of graphing calculators (International Society for Technology in Education, 2008). "Many [teachers] still cling to the idea that one must be able to do the mathematics by hand in order to understand and use it" (Singletary, 2009, p.391). These teachers believe that the introduction of the calculator is only appropriate once the mathematics by hand is mastered (Singletary, 2009). Therefore, many teachers would like to use graphing calculators as an extension for learning, and not a new way of teaching the concepts.
Important Findings on Student Outcomes
Teachers use graphing calculators as a way for students to explore more conceptual understanding of the mathematics concepts. It is believed that the use of calculators allows more interactive and exploratory learning environments which leads to a deeper understanding of the underlying concepts. Teachers have noticed that, "graphing calculators can empower students to be better problem solvers" (Dunham, 1994, p.444). Most all studies of graphing calculator use have come back very positive. "Research shows that calculator use does not undermine computational ability while it does improve problem-solving and conceptual understanding" (Singletary 2009).
In 2008, a study was done about the use of graphing calculators on high school exams. It reported the impact of using a graphing calculator on a test rather than having only a scientific calculator and needing to do graphing my hand. The study categorized exam questions into four categories. It was concluded that each category of questions was testing different sets of skills, and it was important to have all types of questions on exams to allow for the different assessments. Also, the majority of questions fell into two categories that were considered to be routine in nature, so there was no evidence that the exams have increased in difficulty because of the requirement of the graphing calculator (Brown, 2008).
One limitation of the graphing calculator was discussed in a 2004 article by Weiss. Certain graphs can look misleading depending on how the viewing window is set up. In the article, there was a picture of a viewing window of a graphing calculator that displayed a sin graph and appeared to have two periods. In reality, it was a graph of sin(190x), which has 190 periods. Even if the viewing screen was set at the maximum number of intervals allowable by the calculator, it still would not have showed all 190 periods (Weiss, 2004). Some of this confusion can be avoided if these limitations are discussed with students prior to facing the restriction. However, this is one reason it is necessary that students have a general knowledge of graphs and how they function prior to using a graphing calculator.
Emerging Trends and Open Issues
In 1993 there was a survey done of teachers and their thoughts about calculators. The article concluded that, "More teachers were against the use of calculators on tests than were for their use" (National Council of Teachers of Mathematics, 1993). The survey suggested there was some indecision on the part of the math teachers, because they liked the idea of letting the students use calculators for all homework assignments, but did not want the same for all tests. Compare that scenario to today, when the majority of Algebra II classes require the use of graphing calculators. There has clearly been a dynamic switch in the use of graphing calculators in curricula within the past 10 years. Teachers have always thought that, "this technology holds unlimited potential for significantly changing both what is taught and how it is taught" (National Council of Teachers of Mathematics, 1993, p.261). However, it is only now that there has been a substantial integration into state's mathematics curriculum, to where exams require the use of a graphing calculator.
Overall, the graphing calculator has proved to be a very helpful and effective tool. It is being used as an integral part of high school mathematics and is helping students better understand both mathematics and science concepts. These concepts will help prepare students for college classes and for jobs in the workplace after graduation.
References
Brown, R. (2008). Graphing and graphing calculators in examinations. Research in mathematics education, 10, 1, 91-92.
Dunham, P. H. (1994). Research on Graphing Calculators. The mathematics teacher, 87, 6, 440-445.
International Society for Technology in Education. (2008). Graphing Calculators. Learning and leading with technology, 36, 1, 40-41.
National Council of Teachers of Mathematics. (1993). Graphing Calculators. The mathematics teacher, 86, 9, 782.
National Council of Teachers of Mathematics. (1993). Reader Reflections: Graphing Calculators, 86, 3, 261.
National Council of Teachers of Mathematics. (1994). Applications for Graphing Calculators. The mathematics teacher, 87, 4, 298.
Singletary, T. J. (2009). Graphing Calculator Use in Algebra Teaching. School science and mathematics, 109, 7, 383-393.
Weiss, J. (2004). Trigonometric Identities on a Graphing Calculator. The college mathematics journal, 35, 5, 393-396.
Calculators and Graphing Calculators
Jacque LowryDescription and Uses of Technology
Calculators have been easily accessible for classroom use for over 30 years. Graphing calculators, on the other hand, have only been available for about 20 years and have been an integral part of the curriculum for the majority of classrooms across the country for just over 10 years (Singletary, 2009). Graphing calculators are capable of plotting graphs on the screen, graphing equations, and solving multiple equations simultaneously. They also have download-able programs available that can solve more complex equations (International Society for Technology in Education, 2008). These types of calculators are mostly used for higher level math, such as Algebra II and Calculus.For about a decade, there has been an argument whether or not calculators should be used during math testing. There are still debates between teachers and states on this issue, but many standardized tests and college entrance exams allow the use of graphing calculators (International Society for Technology in Education, 2008). "Many [teachers] still cling to the idea that one must be able to do the mathematics by hand in order to understand and use it" (Singletary, 2009, p.391). These teachers believe that the introduction of the calculator is only appropriate once the mathematics by hand is mastered (Singletary, 2009). Therefore, many teachers would like to use graphing calculators as an extension for learning, and not a new way of teaching the concepts.
Important Findings on Student Outcomes
Teachers use graphing calculators as a way for students to explore more conceptual understanding of the mathematics concepts. It is believed that the use of calculators allows more interactive and exploratory learning environments which leads to a deeper understanding of the underlying concepts. Teachers have noticed that, "graphing calculators can empower students to be better problem solvers" (Dunham, 1994, p.444). Most all studies of graphing calculator use have come back very positive. "Research shows that calculator use does not undermine computational ability while it does improve problem-solving and conceptual understanding" (Singletary 2009).In 2008, a study was done about the use of graphing calculators on high school exams. It reported the impact of using a graphing calculator on a test rather than having only a scientific calculator and needing to do graphing my hand. The study categorized exam questions into four categories. It was concluded that each category of questions was testing different sets of skills, and it was important to have all types of questions on exams to allow for the different assessments. Also, the majority of questions fell into two categories that were considered to be routine in nature, so there was no evidence that the exams have increased in difficulty because of the requirement of the graphing calculator (Brown, 2008).
One limitation of the graphing calculator was discussed in a 2004 article by Weiss. Certain graphs can look misleading depending on how the viewing window is set up. In the article, there was a picture of a viewing window of a graphing calculator that displayed a sin graph and appeared to have two periods. In reality, it was a graph of sin(190x), which has 190 periods. Even if the viewing screen was set at the maximum number of intervals allowable by the calculator, it still would not have showed all 190 periods (Weiss, 2004). Some of this confusion can be avoided if these limitations are discussed with students prior to facing the restriction. However, this is one reason it is necessary that students have a general knowledge of graphs and how they function prior to using a graphing calculator.
Emerging Trends and Open Issues
In 1993 there was a survey done of teachers and their thoughts about calculators. The article concluded that, "More teachers were against the use of calculators on tests than were for their use" (National Council of Teachers of Mathematics, 1993). The survey suggested there was some indecision on the part of the math teachers, because they liked the idea of letting the students use calculators for all homework assignments, but did not want the same for all tests. Compare that scenario to today, when the majority of Algebra II classes require the use of graphing calculators. There has clearly been a dynamic switch in the use of graphing calculators in curricula within the past 10 years. Teachers have always thought that, "this technology holds unlimited potential for significantly changing both what is taught and how it is taught" (National Council of Teachers of Mathematics, 1993, p.261). However, it is only now that there has been a substantial integration into state's mathematics curriculum, to where exams require the use of a graphing calculator.Overall, the graphing calculator has proved to be a very helpful and effective tool. It is being used as an integral part of high school mathematics and is helping students better understand both mathematics and science concepts. These concepts will help prepare students for college classes and for jobs in the workplace after graduation.
References
Brown, R. (2008). Graphing and graphing calculators in examinations. Research in mathematics education, 10, 1, 91-92.
Dunham, P. H. (1994). Research on Graphing Calculators. The mathematics teacher, 87, 6, 440-445.
International Society for Technology in Education. (2008). Graphing Calculators. Learning and leading with technology, 36, 1, 40-41.
National Council of Teachers of Mathematics. (1993). Graphing Calculators. The mathematics teacher, 86, 9, 782.
National Council of Teachers of Mathematics. (1993). Reader Reflections: Graphing Calculators, 86, 3, 261.
National Council of Teachers of Mathematics. (1994). Applications for Graphing Calculators. The mathematics teacher, 87, 4, 298.
Singletary, T. J. (2009). Graphing Calculator Use in Algebra Teaching. School science and mathematics, 109, 7, 383-393.
Weiss, J. (2004). Trigonometric Identities on a Graphing Calculator. The college mathematics journal, 35, 5, 393-396.
Reviewed By: (Mike Hittle, Brenda Courtad)